JERUSALEM — At first it didn’t seem unusual when the faces of the Hamas leadership turned up on the group’s TV network. But then they were shot down, one by one, while a message warned that Hamas’ time was running out.

Even as Israel’s armor and foot soldiers push into the Gaza Strip in an effort to stop militants from launching rockets into Israel, the war is also being waged with psychological operations designed to sap morale on both sides.

Over at Islamic Jihad’s Voice of Jerusalem radio station in Gaza City, broadcaster Kamal Abu Nasser said that at least once an hour, the Israeli military also breaks into his signal and broadcasts messages blaming Hamas for everyone’s problems.

Hamas, for its part, said it has broadcast messages on Israeli military walkie talkies threatening to kidnap and kill Israeli soldiers. The army said it had no information on such transmissions.

The fate of Sgt. Gilad Schalit, who was captured by Hamas-linked militants in 2006 and whose whereabouts remain unknown, is repeatedly evoked in broadcasts and statements by Hamas, which has several times has threatened to nab more Israeli soldiers. Hamas tried to spread rumors that it had captured several. At least one actual attempt failed, the military said.

Israeli military spokesman Brig. Gen. Ilan Tal said he would not comment on Israel’s psychological operations.

“If we’re talking about psychological warfare, we have to learn from what Hamas is doing,” he said. “We expect Hamas to intensify and increase those sort of rumors (of kidnappings) as the situation gets more critical.” Hamas’ ruses extend into the battlefield as they try to combat Israel’s overwhelming military advantage.

Military spokesman Maj. Avital Leibovich told The Associated Press that Israel’s forces have found Gaza’s neighborhoods to be riddled with booby traps, including mannequins placed at apartment entrances and rigged to explode when the soldiers approach.

Israel’s army formed a psychological operations unit three years ago, though its initial efforts in the 2006 Lebanon war were largely restricted to drawing satirical cartoons of Hezbollah leader Hassan Nasrallah and dropping them as leaflets over southern Lebanon.

More chilling at the time for Beirut residents, however, were the strange phone calls they received during the war telling them that their woes were due to Hezbollah and they should turn against the guerrillas.

That particular technique has reappeared in the current Gaza onslaught, with phone calls and leaflets telling Gazans that their problems were due to Hamas. The leaflets include a phone number and e-mail address to call in tips about the whereabouts of militant leaders and weapons caches.

Ephraim Kam, the deputy director of Tel Aviv University’s Institute of National Security Studies, said the role of psychological operations loomed large in this offensive, more so than in the past.

“I think we did this in former wars, but in this case we had a lot of time, relatively speaking, and so much more emphasis was given to psychological warfare,” Kam said.

Lacking resources, Hamas’ psychological efforts have been largely restricted to the propaganda broadcasts on its own Al Aqsa TV channel, including Hebrew language messages asking Israelis to “choose between a peace that gives us back our rights or a war that will smash you down.” There have also been reports of threatening text messages sent to the inhabitants of Israel’s southern towns telling them to hide underground because Hamas is coming for them.

The biggest weapon in Hamas’ psychological arsenal is also its best known actual weapon — the homemade rockets it sends on erratic paths into southern Israeli towns. During the conflict, militants have also used longer-range Grad rockets, hitting cities that used to be out of range.

The thousands of rockets have only killed only a handful of Israelis, yet life across Israel’s south has been paralyzed.

The greatest disinformation coup of the conflict so far, however, came right at the beginning of the offensive when Israeli bombers caught hundreds of Hamas security men inside their compounds.

The day before a massive Israeli airstrike, Israeli military radio channels broadcast talk of a “lull” and pulled troops back from the border.

Israeli defense officials now say it was a psychological warfare tactic or a “con” to lure Hamas fighters out of hiding.